2019/09/14 by Marlina Slamet, Slamet, Marlina, Viraht Sahni +1
Chemistry · Computer Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.1909.09701
openalex publication_date 2019/09/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The Schr "odinger-Pauli theory of electrons in the presence of a static\nelectromagnetic field can be described from the perspective of the individual\nelectron via its equation of motion or `Quantal Newtonian' first law. The law\nis in terms of `classical' fields whose sources are quantum-mechanical\nexpectation values of Hermitian operators taken with respect to the wave\nfunction. The law states that the sum of the external and internal fields\nexperienced by each electron vanishes. The external field is the sum of the\nbinding electrostatic and Lorentz fields. The internal field is the sum of\nfields representative of properties of the system: electron correlations due to\nthe Pauli exclusion principle and Coulomb repulsion; the electron density;\nkinetic effects; the current density. Thus, the internal field is a sum of the\nelectron-interaction, differential density, kinetic, and internal magnetic\nfields. The energy can be expressed in integral virial form in terms of these\nfields. Via this perspective, the Schr "odinger-Pauli equation can be written\nin a generalized form which then shows it to be intrinsically self-consistent.\nThis new perspective is explicated by application to the triplet 23S state\nof a 2-D 2-electron quantum dot in a magnetic field. The quantal sources of the\ndensity; the paramagnetic, diamagnetic, and magnetization current densities;\npair-correlation density; the Fermi-Coulomb hole charge; and the\nsingle-particle density matrix are obtained, and from them the corresponding\nfields determined. The fields are shown to satisfy the `Quantal Newtonian'\nfirst law. The components of the energy too are determined from these fields.\nFinally, the example is employed to demonstrate the intrinsic self-consistent\nnature of the Schr "odinger-Pauli equation.\n